Resistance Department of Physics & Astronomy Texas Christian University, Fort Worth, TX April 23, 2013 1 Introduction Electrical resistance is a measure of how much an object opposes (or resists) the flow of current. Resistance is not a fundamental property of a material, but depends on the size and shape of the resistor. For a resistor with uniform cross-sectional area, the resistance is given by R = ρ L A, (1) where L is the distance the current flows through, A is the cross-sectional area of the resistor, and ρ is the resistivity. Unlike resistance, resistivity is a fundamental property of the material that quantifies how hard it is for current to flow through the material. Resistivity does not depend on the size or shape of the resistor, it is a property of the substance that makes up the resistor. Changing the size of a resistor will change its resistance, but not its resistivity. Resistors are devices that are commonly used in electrical circuits and they can be combined within the circuit in two different ways. Resistors that are connected in series share a single connection; one terminal of one resistor is connected to one terminal of the other resistor. The remaining terminal on each resistor is connected to some other electrical device. The total resistance of two resistors connected in series is R t = R 1 + R 2, (2) where we simply add the resistances of the two individual resistors. Resistors can also be connected in parallel. In this case, the resistors are share two connections; both terminals of one resistor are connected to the two terminals of the other resistor. For resistors connected in parallel, the total resistance is found by adding reciprocals, 1 R t = 1 R 1 + 1 R 2. (3) As you look at the front panel of the multimeter, you will notice that there are black and red jacks. Also on your workbench you may find red and black cables. It is a common practice to use a red wire for high voltage or positive signal and a black wire for low voltage, ground, or negative signal. We suggest that you use this system in the laboratory since it is helpful in checking the wiring. (A different system is used in the wiring of buildings. White denotes the neutral wire; black is used to indicate wires under 120 V AC; red is reserved for 240 V. Green is always used for ground wires.) 1
2 Equipment Multimeter, breadboard, resistors, strips of high resistance paper 3 Procedure 1. Set the meter to measure resistance (ohm, Ω) by depressing the HI Ω function switch. Connect a black lead to the common jack of the multimeter and a red lead to the A-Ω jack. Select the 1000 range. Note that HI Ω range is set to measure kiloohms, kω, combining it with the 1000 range means that the maximum value to be measured is 1, 000, 000 Ω or 1 MΩ. Keep the leads apart and the display should flash. The flashing indicates that the measured resistance between two leads exceeds the maximum value of 1 MΩ. 2. Grasp the two exposed leads, holding one in your right hand and the other in the left hand. The meter will show the resistance of your body. Have your partner measure the resistance of his/her body. Record the results in the data sheet. 3. Measure the resistance of your skin by touching two points on your skin about 2 inches apart. The resistance of skin may vary greatly with the amount of moisture on the skin. If your skin is dry you may have to change the range from 1000 kω to 10 MΩ. If it is wet, you can display more significant digits by changing the range to 100 kω. Compare the skin resistance of your palm to the skin resistance on your arm. Record your results in the data sheet. 3.1 Resistivity 1. You will be given several strips of high resistance paper of various sizes. Use the ohmmeter setting of your multimeter (in the HI Ω range) to measure the resistance of each strip. Be sure to place the probes on the edges of the paper. 2. Measure the resistance using the other two edges. 3. Measure the length and width of the strips and record the results in the table on the data sheet. The thickness of the paper is 0.25 mm. Carefully think about which dimensions are used to calculate the cross-sectional area for different orientations of the paper. 4. Determine the resistivity of the paper using Eq. (1). 3.2 Resistance 1. Connect a resistor between two posts on the breadboard (Fig. 1, left). The breadboard allows you to build electrical circuits. The openings are designed to fit banana plugs and are arranged in the form of squares. There are nine openings per square. They are all connected internally, but separate squares are isolated. To build a circuit you need to plug in one end of the resistor into any opening in one square and another end into another square. An example is shown in Fig. 1. The center image shows an example of a GOOD connection where resistor is mechanically attached to a banana plug, which is pushed into holes in adjacent squares. The leads are pushed into other holes in the same squares and a multimeter. You can read a measured value on the display. An example of a BAD connection is shown below. In this 2
Figure 1: The breadboard. A breadboard (left) and examples of a good circuit (center) and a bad circuit (left). photo the black lead is attached to a square with no resistor attached and the display is blank. This circuit is open and the multimeter cannot measure anything. 2. For your convenience, we attached the resistors to banana plugs. There are five different banana plugs with different resistors provided for each setup. The resistors are marked with four or five colour bands. This is the resistor colour code. The first two bands indicate two significant digits, the third indicates the power of ten, and the fourth band indicates the precision of the measurements. The fifth band (if present) indicates reliability. The colour code key for resistors is given in Table 1. Always orient the resistors so that the gold or silver band, the so called tolerance or precision band, are on your right side. For example, a resistor with the following colors (from left to right), brown black red - gold tells us the first digit is 1 (brown), the second digit is 0 (black) and the power of ten is 2 (red). That gives us R = 10 10 2 Ω = 1000 Ω. The gold band tells us that this is accurate to within 5%, so the actual resistance could range from 950 Ω to 1, 050 Ω. 3. Attach the meter leads to the breadboard and record the displayed values. DO NOT ATTACH ANYTHING TO THE 10 A PLUG OF THE MULTIMETER. Change the range so that the display will show all four digits. For resistance values less then 10 Ω depress the LO Ω and 10 Ω switches. Clip the test leads together. You may observe a non-zero reading (a few tenths of an ohm). The reading is due to the resistance of the test leads, fuses, and jacks. You may subtract the value from any readings in this range, if such accuracy is required. Report the measured resistance values in a table and compare the data with the values expected from the color code. Compare the difference with the estimated value from the fourth band of the color code. 3
Table 1: Resistor color code. First three bands Black 0 Brown 1 Red 2 Orange 3 Yellow 4 Green 5 Blue 6 Violet 7 Gray 8 White 9 Tolerance band Silver 10% Gold 5% No band 15% 3.3 Resistors in series 1. Select two resistors of similar values. Measure each resistance. 2. Connect the resistors in series (only one connection between the two resistors) on the bread board as shown in Fig. 2. In the left photo the resistors are plugged into adjacent squares, in the photo on the right the resistors are connected to distant squares and a white bridging plug is used to connect them. There are many other possible arrangements of resistors on the breadboard resulting in a series combination. Record the resulting resistance. 3. Compare the measured and expected values of two resistors connected in series. Report the experimental and theoretical values in a table. 4. Repeat the measurement with other combinations of resistors. 3.4 Resistors in parallel 1. Measure the individual resistance of two resistors. You may use the same resistor combinations used in the previous experiment. 2. Connect the two resistors in parallel (two connections between the resistors) as shown in Fig. 3. The photo shows one of many possible arrangements of the resistors on the breadboard that give the parallel combination. You may want to explore and build your own connections. Make your own arrangement of resistors in parallel. 3. Compare the readings of the meter with the theoretical value. Compute the percentage difference and report the experimental and theoretical data in a table. 4. Repeat the measurements for other combinations of resistors. 4
9 9 9 9 1 R 2 Figure 2: Resistors in series. The series circuit shown schematically at the top can be can wired in a number of different ways. The above photographs show two possible series combinations. Figure 3: Resistors in parallel. The photo on the right shows one possible arrangement of resistors in parallel as shown schematically on the right. 5
4 Report In your report discuss the following: 1. The high-resistance paper has a resistivity of 1.25 Ω m. How do your values compare? What are possible causes for discrepancies between the known value and your calculated values? 2. What are possible causes for discrepancies between theoretical and measured values of resistors in series and in parallel? 3. When it is practical to connect resistances in series and when in parallel? 6